Question

product of roots of the equation
$5{x}^{2} - 4x + 2 + k(4 {x}^{2} - 2x - 1) = 0$
is 2.
then find k​

Answer 1

Solution :-

Given Equation can be written as

→ 5x² - 4x + 2 + 4x²k - 2xk - k = 0

→ (5x² + 4x²k) + (-4x - 2kx) + (2 - k) = 0

→ (5 + 4k)x² + (-4 - 2k)x + (2 - k) = 0

→ (5 + 4k)x² - (4 + 2k)x + (2 - k) = 0

Now, comparing with ax² + bx + c = 0, we get,

• a = (5 + 4k)
• b = (4 + 2k)
• c = (2 - k)

Now, we know that, product of roots is (c/a) .

Therefore,

→ (c/a) = 2

→ (2 - k) / (5 + 4k) = 2

→ 2 - k = 2(5 + 4k)

→ 2 - k = 10 + 8k

→ - k - 8k = 10 - 2

→ - 9k = 8

→ k = (-8/9) (Ans.)